Question

An illustration shows a triangle with a base labeled 8 inches. A line runs through the center of the triangle from the apex to the base. This perpendicular height is labeled 5 inches.
Crystal cuts a piece of wood into the shape of a triangle. The height of the triangle is 5 inches, and the base of the triangle measures 8 inches. Crystal makes a scale drawing of the triangle. If the height of her scale drawing is 2 inches, what is the area of her scale drawing?

(1 point)
Responses

6.4 square inches
6.4 square inches

20 square inches
20 square inches

1.6 square inches
1.6 square inches

3.2 square inches

Answer 1

To find the area of Crystal's scale drawing of the triangle, we first need to calculate the area of the original triangle.

The formula for the area of a triangle is:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

For the original triangle:
- Base = 8 inches
- Height = 5 inches

Substituting these values into the formula:

\[
\text{Area} = \frac{1}{2} \times 8 \times 5 = \frac{1}{2} \times 40 = 20 \text{ square inches}
\]

Next, we need to determine the area of the scale drawing. The height of the scale drawing is 2 inches, and the original height is 5 inches, indicating a scaling factor. The scale factor can be found by comparing the heights:

\[
\text{Scale factor} = \frac{\text{height of scale drawing}}{\text{height of original triangle}} = \frac{2}{5}
\]

Since the area scales with the square of the linear dimensions, the area of the scale drawing can be calculated using the square of the scale factor:

\[
\text{Area of scale drawing} = \text{Area of original triangle} \times \left(\text{Scale factor}\right)^2
\]

Calculating the area of the scale drawing:

\[
\text{Area of scale drawing} = 20 \times \left(\frac{2}{5}\right)^2 = 20 \times \frac{4}{25} = 20 \times 0.16 = 3.2 \text{ square inches}
\]

Therefore, the area of Crystal's scale drawing is **3.2 square inches**.